There's a downloadable issue of Vinyar Tengwar
http://www.elvish.org/VT/VT43sample.pdf which contains Tolkien's translations of the Lord's Prayer & the Ave Maria. Tolkien uses 'Eru' to translate 'God'.
For what its worth - Tolkien seems to have considered the two words equivalent - only
really stubborn & awkward people would deny that
However, I'm not sure that actually proves anything, or contributes very much...